Advertisements
Advertisements
Question
In drilling world’s deepest hole it was found that the temperature T in degree celcius, x km below the earth’s surface was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?
Solution
T = 30 + 25(x – 3), 3 ≤ x ≤ 15
Where, T = temperature and x = depth inside the earth
The Temperature should be between 155°C and 205°C.
So, we get,
⇒ 155 < T < 205
⇒ 155 < 30 + 25(x – 3) < 205
⇒ 155 < 30 + 25x – 75 < 205
⇒ 155 < 25x – 45 < 205
Adding 45 to each term, we get
⇒ 200 < 25x < 250
Dividing each term by 25, we get.
⇒ 8 < x < 10
Hence, temperature varies from 155° C to 205° C at a depth of 8 km to 10 km.
APPEARS IN
RELATED QUESTIONS
Solve: 4x − 2 < 8, when x ∈ N
−(x − 3) + 4 < 5 − 2x
\[\frac{2\left( x - 1 \right)}{5} \leq \frac{3\left( 2 + x \right)}{7}\]
\[\frac{x}{x - 5} > \frac{1}{2}\]
Solve each of the following system of equations in R.
1. x + 3 > 0, 2x < 14
Solve each of the following system of equations in R.
3x − 1 ≥ 5, x + 2 > −1
Solve each of the following system of equations in R.
11 − 5x > −4, 4x + 13 ≤ −11
Solve each of the following system of equations in R.
2 (x − 6) < 3x − 7, 11 − 2x < 6 − x
Solve each of the following system of equations in R.
20. −5 < 2x − 3 < 5
Solve \[\frac{1}{\left| x \right| - 3} < \frac{1}{2}\]
Solve \[\frac{\left| x + 2 \right| - x}{x} < 2\]
Solve
\[\left| \frac{2x - 1}{x - 1} \right| > 2\]
Solve \[\left| x - 1 \right| + \left| x - 2 \right| + \left| x - 3 \right| \geq 6\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
Mark the correct alternative in each of the following:
If x is a real number and \[\left| x \right|\]\[<\]5, then
Mark the correct alternative in each of the following:
If \[\left| x + 2 \right|\]\[\leq\]9, then
Solve `(x - 2)/(x + 5) > 2`.
Solve the following system of inequalities:
`x/(2x + 1) ≥ 1/4, (6x)/(4x - 1) < 1/2`
If |x + 3| ≥ 10, then ______.
If x ≥ –3, then x + 5 ______ 2.
Solve for x, the inequality given below.
`(|x - 2| - 1)/(|x - 2| - 2) ≤ 0`
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?
State which of the following statement is True or False.
If xy < 0, then x < 0 and y < 0
If x < –5 and x > 2, then x ∈ (– 5, 2)
If `(-3)/4 x ≤ – 3`, then x ______ 4.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
